Antonymy and Evaluativity
Jessica Rett
Rutgers University
1. Introduction
The goal of this paper is to characterize and account for the systematic distribution
of a semantic property, “evaluativity”. A construction is evaluative if it makes
reference to a degree that exceeds a contextually specified standard. The term
comes from Neeleman et al. (2004); Seuren (1978) alternatively refers to this
property as ‘orientedness’ and Bierwisch (1989) as ‘norm-relatedness’. The
distribution of evaluativity seems to vary with the predicate and quantifier of a
degree construction. I attempt to explain this distribution in terms of semantic
properties of predicates and degree quantifiers.
Evaluativity is typically associated with positive constructions as in (1):
(1).
a. Amy is tall.
b. Amy is a tall woman.
I use the term ‘degree construction’ to refer to any construction that makes
reference to a degree of gradability or a degree of quantity. I use the term ‘degree
morphology’ to refer to morphemes that bind or saturate degree variables:
examples include measure phrases (MPs) like 5ft and degree quantifiers like the
comparative morpheme –er and the wh-phrase how.
A positive construction is a degree construction without any overt degree
morphology. (1a) is evaluative because it attributes to Amy a height that exceeds a
relevant standard. This illustrates the context-sensitivity of evaluativity; evaluative
constructions refer to a standard, and this standard can vary with the context of
utterance. Amy can be considered tall in one context, e.g. a discussion of
ballerinas, and short in another, e.g. a discussion of basketball players.1
Another property of evaluativity is that it is not part of the meaning of an
adjective. The fact that a positive construction with the adjective tall is evaluative
does not bear on the evaluativity of other degree constructions with tall:
(2)
a. Amy is taller than Betty.
b. Amy is as tall as Betty.
Thanks foremost to Roger Schwarzschild, as well as Chris Barker, Jonathan Bobaljik, Daniel
Büring, Sam Cumming, Jane Grimshaw, Hans Kamp, David Kaplan, Chris Kennedy, Nathan
Klinedinst, Angelika Kratzer, Roumyana Pancheva, and Chris Potts. This paper also benefitted
from comments from audiences at the Rutgers Semantics Group; the University of Massachusetts,
Amherst; Princeton University; UCLA and SALT 17.
1
For a discussion of how this standard is valued, see Kennedy 2007 and references therein.
© 2007 by Jessica Rett
T. Friedman and M. Gibson (eds), SALT XVII 210-227, Ithaca, NY: Cornell University
Antonymy and Evaluativity
The comparative in (2a) and the equative in (2b) contain the predicate tall, but
these sentences are not evaluative. An utterance of e.g. (2b) does not make
reference to a degree that exceeds a contextual standard: (2b) could felicitously be
uttered if Amy’s and Betty’s heights were below the relevant standard of tallness.
We can test the evaluativity of a degree construction in a general sense by
determining whether or not it entails its corresponding positive construction
(Bierwisch 1989). Because evaluativity is context-sensitive, this notion of
entailment is one that requires holding fixed the context of utterance, and thus the
contextually-valued standard, across the two constructions: ! entails " iff for
every context c, if ! is true at c then so is ". We can verify that (2a) is not
evaluative because it does not entail that Amy (or Betty) is tall.
As evaluativity is not a part of the meaning of the predicate in a
construction, neither is it a part of the meaning of the construction.
(3).
a. Amy is as tall as Betty.
b. Amy is as short as Betty.
The equative (3a) is not evaluative, but the equative in (3b) is: it makes reference
to a contextually salient standard of shortness (and entails that Amy is short).
I argue in this paper that the distribution of evaluativity is a product of two
things: the polarity of the predicate and the nature of the degree quantifier
(whether it is ‘polar-variant’ or ‘polar-invariant’). I’ll first establish a major
shortcoming of current accounts of evaluativity, and then propose that evaluativity
is encoded in a degree modifier, which can optionally occur in any degree
construction. Section 6 extends the account to antonym pairs that demonstrate
evaluativity patterns different from tall and short.
2. Analyses of Evaluativity
As we have seen above, what seems to be the most simple use of adjectives (the
positive construction) has an aspect of meaning (evaluativity) that is often lacking
in more complex constructions like the comparative. The question of how to go
about encoding evaluativity in the positive construction has thus been centered on
how to associate the presence of a semantic property with the absence of any
additional morphology (and, similarly, the absence of a semantic property with the
presence of additional morphology).
The MP construction in (4) has two overt arguments: an individual (the
subject Amy) and a degree (the MP 5ft). This suggests the semantics for tall in (5);
I assume here that if x is tall to degree d, then x is tall to degree d – 1.
(4)
(5)
Amy is 5ft tall.
[[tall]] = !x!d.tall(x,d)
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This is a common view of the semantics of gradable adjectives (Seuren
1978, Rullman 1995, Heim 2000) and I will use it in what follows. An alternative
view holds that gradable adjectives are ‘measure functions,’ functions from
individuals to degrees (Kennedy 1999, 2007, a.o.). A vague predicate analysis
eliminates reference to degrees entirely, assuming that adjectives are functions
from objects to truth values on a partitioned contextually-sensitive domain
(McConnell-Ginet 1973, Kamp 1975, Klein 1980).
The apparent correlation between the presence of evaluativity and the
absence of degree morphology suggests prima facie that an analysis of the positive
construction should link the two. This has led many to argue that the positive
construction contains a covert degree phrase (POS). POS simultaneously binds the
free degree variable and compares the degree to a standard (Bartsch and
Vennemann 1972, Cresswell 1976, von Stechow 1984, Kennedy 1999). The
meaning in (6) is one instantiation of POS, based on Cresswell’s analysis.
(6)
POS = !P!x∃d.P(x,d) ∧ d > s
In recent accounts (Kennedy 1999, 2007), POS resides in the head of DegP
in lieu of an MP. So POS resolves the differences between positive and MP
constructions at once: it accounts for the difference in overt arguments (it covertly
binds the degree argument in the positive construction), and it contributes
evaluativity by restricting the degrees to those high on a scale with respect to a
standard. POS can’t cooccur with overt degree morphology because both
operators reside in Deg° and because both operators bind the degree argument.
But, as we have seen, it is false that overt degree morphology blocks
evaluativity. In (3b), the equative construction is evaluative despite the presence
of the degree quantifier as. A similar pattern is exhibited in degree questions ([+/–
E] marks an evaluative and a non-evaluative construction respectively).
(7)
a. How tall is Amy?
[–E]
b. How short is Amy?
[+E]
While the question in (7a) comes with no expectation that Amy be particularly
tall, the question in (7b) presupposes that Amy is in fact short.
The table in (8) is a summary of the distribution of evaluativity in
constructions with overt degree morphology. Comparative and excessive
constructions are not evaluative (do not entail that x is A), nor are equatives and
interrogatives with positive antonyms; but equatives and interrogatives with
negative antonyms are evaluative.
I’ll call those constructions whose evaluativity depends on the polarity of
the antonym ‘polar-variant’ constructions. Those whose evaluativity does not
depend on the polarity of the antonym are ‘polar-invariant’.
Antonymy and Evaluativity
(8)
The distribution of evaluativity in constructions with degree morphology
type
form
tall short ex.
[−E] [+E] Amy is as tall/short as Betty.
polar-variant equative
interrogative [−E] [+E] How tall/short is Betty?
[−E] [−E] Amy is too tall/short for her pants.
polar-invariant excessive
comparative [−E] [−E] Amy is taller/shorter than Betty.
It seems then that the POS account does not accurately describe the
distribution of evaluativity. The data above call for an analysis of evaluativity that
i) allows for evaluativity to cooccur with overt degree morphology, and ii) can
account for its absence in constructions with positive-polarity predicates and in
constructions like the comparative.
3. The Degree Modifier EVAL
We can allow for evaluativity to cooccur with overt degree morphology by
encoding it in a degree modifier of type !!d,t",!d,t"". Because modifiers do not
change the type of a construction, they can in principle occur optionally in any
degree construction.
Evaluative constructions reference degrees that exceed a standard. So we
can think of the degree modifier that encodes evaluativity, ‘EVAL’, as a function
from a set of degrees to a subset of those degrees (the ones above the standard).
(9)
EVALi ! !D!d,t"!d. D(d) ∧ d > si!
!
s is a pragmatic variable, i.e. it is left unbound in the semantics. I assume that each
instance of EVAL in a sentence introduces a single pragmatic variable.
The tree below demonstrates how EVAL can contribute evaluativity to the
positive construction (I have yet to argue for why it must):
(10)
a. Amy is tall.
#d.tall'(a,d) ∧ d > s1
b.
NP1
Amy
#d.tall'(x,d) ∧ d > s1
#d.tall'(x,d)
!x
EVAL1
t1
tall
#x#d.tall'(x,d)
This derivation results in a set of degrees. I assume that, in lieu of an overt
quantifier or modifier, the free variable d is bound by existential closure, resulting
in the proposition that Amy is tall to a degree which exceeds the relevant standard
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of tallness. This last move is necessary because to analyze any constituent of the
sentence in (10) as involving quantification over degrees is to prevent its
compatibility with degree quantifiers and modifiers (Doetjes 1997).
Following Bhatt & Pancheva (2004) a.o., the subject Amy is basegenerated in the functional projection “aP,” which takes AP as its complement.
Given a situation in which Amy is 5ft tall and the standard of tallness applicable
to Amy is 3ft, then the argument of EVAL in (10b) includes the degrees 1ft, 2ft,
3ft, 4ft, 5ft, and the value includes 4ft, 5ft but not degrees below 4ft (the sets are
dense). This allows two different mechanisms for resolving the two differences
between the constructions in (4): the difference in arguments is resolved by
existential closure, and the difference in evaluativity is resolved by EVAL.
4. The Distribution of EVAL
The characterization of EVAL as a degree modifier predicts that it can take any
set of degrees as its argument. Due to the fact that EVAL is phonologically covert,
this leads to a state of affairs in which any degree construction can in principle
have an evaluative or non-evaluative interpretation. When either interpretation is
available, the construction is [–E]. When the non-evaluative interpretation is
blocked, the construction is [+E].
As (8) suggests, there are two semantic aspects of degree constructions
that conspire to determine whether or not that construction receives an evaluative
interpretation: 1) the polarity of the predicate in the construction, and 2) whether
or not the construction is polar-invariant. I’ll review the significance of these
properties and discuss how they effect evaluativity in constructions with overt
degree morphology, and then in positive constructions (Section 4.3).
4.1. Polarity
It has been widely observed that two antonyms (e.g. tall and short) make use of
the same scale, but in reverse directions (Cresswell 1976, Seuren 1984, von
Stechow 1984, Bierwisch 1989, Kennedy 1999). The fact that tall and short differ
only in their ordering is illustrated by the following entailment patterns:
(11)
a. Amy is taller than Betty. "
b. Amy is shorter than Betty. "
Amy is not shorter than Betty.
Amy is not taller than Betty.
In (11), the comparative form with the positive antonym tall entails the negation
of the one with the negative antonym short, and vice-versa.
I assume here with Bartsch & Vennemann (1972) and Bierwisch (1989)
that adjectival scales are triples !D,<Υ,$" with D a set of degrees, <Υ a total
Antonymy and Evaluativity
215
ds to which A is tall
5ft
4ft
3ft
2ft
7ft
6ft
4ft
3ft
t h a n
8ft
5ft
t a l l e r
6ft
t h a n
7ft
s h o r t e r
8ft
ds to which A is short
ordering on D, and $ a dimension (e.g. ‘height’). Antonym scales are illustrated in
Figure 1 for the antonyms tall and short:
2ft
1ft
1ft
Figure 1: Amy’s height
I will represent a set of degrees associated with the predicate tall as Dtall
and so forth. Assuming that Amy is 5ft tall, we can represent Amy’s height as it is
reflected on the ‘tall’ scale as well as on the ‘short’ scale:
(12)
a. Amy’s tallness: {1ft, 2ft, 3ft, 4ft, 5ft}tall
b. Amy’s shortness: {5ft, 6ft, 7ft, 8ft, 9ft, …}short
Notice that the set of degrees to which Amy is tall and the set of degrees to which
Amy is short have an endpoint in common. This is a factor of their antonymy.
(13)
(14)
For all adjectives A, A' and for all x in the domain of A, A',
A and A' are antonyms iff: MAX [A(x)] = MAX [A' (x)]
∧ A(x) # A'(x) = {MAX (A(x))},
Where MAX is defined relative to the direction of the scale:
Let D be a set of degrees ordered by the relation <Υ, then
MAX(D) = $d[d ∈ D ∧ ∀d' ∈ D [d' %Υ d ] ]
The fact that the two antonyms share an endpoint and are otherwise complements
is one important characteristic of antonyms for evaluativity: we can reliably infer
from Amy’s tallness to Amy’s shortness, and vice-versa.
A second important characteristic of antonyms is the fact that negative
antonyms are marked with respect to positive ones. To support this claim, I will
review some distributional data; for more explanatory accounts (ones that
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correlate semantic markedness with morphological markedness), see Sapir (1949),
Lyons (1977), Rullman (1995) and Heim (2007).
Lyons says, “We tend to say that small things lack size, that what is
required is less height, and so on, rather than that large things lack smallness and
that what is required is more lowness” (Lyons 1977: 275). The conclusion that
follows is that, e.g., “long is unmarked with respect to short because it occurs in a
variety of expressions from which short is excluded” (Cruse 1986: 173). (15)
shows that some positive antonyms can occur with measure phrases, but their
negative counterparts cannot; (16) shows that positive antonyms but not negative
ones can have nominal forms.
(15)
a. This one is 10ft long.
b. *This one is 10ft short.
(16)
a. What is its length?
b. *What is its shortness?
Also see Higgins (1977) for a psycholinguistic study of the interpretational
differences between marked and unmarked adjectives in comparatives. Both
properties of polar antonyms play a role in the distribution of evaluativity.
4.2. Polar-(In)Variance
This section examines polar-(in)variance by studying relevant semantic properties
of the comparative and equative constructions as a case study. The generalizations
made here can be extended to other polar-(in)variant degree constructions.
Equatives are polar-variant while comparatives are polar-invariant. A
symptom of this difference is the difference in the entailment patterns of these two
constructions. For a polar-variant construction, the negative-antonym form entails
its positive-antonym counterpart (17a);2 for a polar-invariant construction, the
negative-antonym form does not entail its positive-antonym counterpart (17b)
(17)
a. Amy is as short as Betty. " Amy is as tall as Betty.
b. Amy is shorter than Betty. # Amy is taller than Betty.
These entailment patterns are due to the fact that the negative-polarity
form in (17a) is true if two conditions hold: i) that Amy and Betty are the same
height, and ii) that Amy and Betty are short. The positive-polarity form in (17a) is
true only if one condition holds: that Amy and Betty are the same height. In
contrast, for the negative form in (17b) to be true, Betty’s height needs to exceed
Amy’s height; and for the positive form in (17b) to be true, Amy’s height needs to
exceed Betty’s height. The difference can be summarized as follows: for polarvariant constructions, the truth conditions of a negative form are a subset of the
2
This is true for how many questions as well, assuming the semantics of questions from
Groenendijk and Stokhof (1984) in which a question Q1 entails a question Q2 iff the denotation of
Q1 is a subset of the denotation of Q2. Thus How short is Amy? " How tall is Amy?
Antonymy and Evaluativity
truth conditions of its corresponding positive form. For polar-invariant
constructions, the truth conditions of a negative-antonym form and its positiveantonym counterpart are contradictory.3
Because of the nature of EVAL (9), the analysis presented here predicts
that each degree construction has an evaluative and a non-evaluative interpretation
available. I’ll first examine polar-variant constructions by discussing what it
means for the equative to be polar-variant.
(18)
(19)
Amy is as tall as Betty.
a. NON-EVALUATIVE: {d":tall'(a,d")} = {d#:tall'(bd#)}
b. EVALUATIVE: {d":tall'(a,d") ∧ d" > s$%&&} = {d#:tall'(b,d#) ∧ d# > s$%&&}
Amy is as short as Betty.
a. NON-EVALUATIVE: {d":short'(a,d")} = {d#:short'(bd#)}
b. EVALUATIVE: {d":short'(a,d") ∧ d" > s'()*$} = {d#:short'(b,d#) ∧ d# > s'()*$}
Here I crucially take the bare equative to have an ‘exactly’ interpretation, rather
than an ‘at least’ interpretation. I’ll return to this assumption in §7. I also assume a
general presupposition that the sets above are non-empty.
Important for the distribution of evaluativity is that the two non-evaluative
interpretations, (18a) and (19a), mean the same thing (are mutually entailing).
(18a) says that Amy’s and Betty’s heights are at the same point on the ‘short’
scale. Given what we know about the relationship between the ‘tall’ and ‘short’
scales, we can infer that for Amy and Betty to satisfy the truth conditions of (18a)
is for Amy and Betty to satisfy the truth conditions of (19a). The synonymy of the
two non-evaluative interpretations is a factor of the first characteristic of polar
antonyms (that we can infer from one scale to the other).
The two evaluative interpretations, (18b) and (19b), do not have the same
meaning because they make reference to the ‘tall’ and ‘short’ standards
respectively. (18b) says that Amy and Betty are of equal height and are tall; (19b)
says that Amy and Betty are of equal height and are short. Given that (18a) and
(19a) have the same truth conditions, and given a (universal) principle that tells
speakers to avoid using a marked form whenever possible, only the positiveantonym version of the two non-evaluative forms is available. This is an effect of
the second characteristic of polar antonyms.
(20)
Amy is as tall as Betty.
(21)
Amy is as short as Betty.
NON-EVALUATIVE
EVALUATIVE
NON-EVALUATIVE
EVALUATIVE
3
For quantifiers like the comparative and the equative, which take two sets of degrees as
arguments, polar-(in)variance could have to do with whether or not the quantifier is symmetric (i.e.
whether Q(A)(B) $ % Q(B)(A). However, this property cannot be generalized to how A, which
displays polar-(in)variance despite its only taking one set of degrees as its argument.
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Jessica Rett
This means that from Amy is as short as Betty we can safely conclude that
Amy is short, as it is unambiguous and the proposition expressed is evaluative.
From Amy is as tall as Betty, we can’t conclude that Amy is tall because this
sentence could be expressing the meaning in (18a), which is unevaluative.
The situation differs for polar-invariant constructions, which I’ll discuss
by examining the comparative. For polar-invariant constructions, the nonevaluative positive-antonym interpretation (22a) and the non-evaluative negativeantonym interpretation (23a) do not have the same truth conditions.
(22)
(23)
Amy is taller than Betty.
a. NON-EVALUATIVE: {d":tall'(a,d")} ⊃ {d#:tall'(b,d#)}
b. EVALUATIVE: {d":tall'(a,d") ∧ d" > s$%&&} ⊃ {d#:tall'(b,d#) ∧ d# > s$%&&}
Amy is shorter than Betty.
a. NON-EVALUATIVE: {d":short'(a,d")} ⊃ {d#:short'(b,d#)}
b. EVALUATIVE: {d":short'(a,d") ∧ d" > s'()*$} ⊃ {d#:short'(b,d#) ∧ d# > s'()*$}
Unlike polar-variant forms, polar-invariant constructions with different
antonyms differ in more than just their evaluativity. With both interpretations of
each comparative, for (22) to be true, (23) must be false and vice-versa. This
means that the non-evaluative negative-antonym form is not blocked, and both
constructions can have either meaning.
(24)
Amy is taller than Betty.
(25)
Amy is shorter than Betty.
NON-EVALUATIVE
EVALUATIVE
NON-EVALUATIVE
EVALUATIVE
This analysis crucially assumes that a [–E] construction can – but need not
– have an evaluative interpretation. This is a harmless assumption. There are two
possible situations in which an ambiguous degree construction (let’s use Amy is as
tall as Betty) could be uttered. The first is one in which the hearer knows that
Amy or Betty are tall relative to the contextually-valued standard. In this case, he
can interpret the utterance to have an evaluative interpretation without running
into any problems. The second situation is one in which the hearer does not know
whether Amy or Betty are tall, in which case he can interpret the utterance to have
a non-evaluative interpretation.
The availability of an evaluative interpretation for a [–E] construction
surfaces in some constructions, although I do not have anything to say on which
constructions and why. Below is a construction in which a [–E] form – a positiveantonym question – is directly juxtaposed with its negative-antonym counterpart.
(26)
a. I don’t know how tall or short Amy is.
b. I don’t know whether Amy is tall or short (or the extent to which).
Antonymy and Evaluativity
219
An intuitive gloss of (26a) is (26b), which gives the positive-polarity question an
evaluative reading. This, I think, speaks in favor of a theory which allows [–E] to
be optionally evaluative.4
To summarize, the distribution of evaluativity among constructions with
overt degree morphology is determined by two factors exhibited by the degree
construction: the polarity of the predicate, and whether or not the construction is
polar-variant. If it is polar-variant, the positive-polarity and negative-polarity
forms differ only insofar as they refer to a contextual standard, rendering a short
non-evaluative interpretation synonymous to a tall non-evaluative interpretation.
This makes these readings subject to a markedness competition and so the nonevaluative reading of the short form is blocked by its tall counterpart. As a result,
negative-polarity polar-variant constructions are [+E], while positive-polarity
polar-variant constructions, as well as polar-invariant constructions, are [–E].
4.3. The Positive Construction
I demonstrated in §3 that EVAL can contribute to the semantics of the positive
construction, but not that it needs to. The theory as I’ve spelled it out predicts that
each of the positive constructions in (27) and (28) can have two possible readings.
(27)
(28)
Amy is tall.
a. NON-EVALUATIVE: ∃d.tall'(a,d)
b. EVALUATIVE: ∃d.tall'(a,d) ∧ d > s$%&&
Amy is short.
a. NON-EVALUATIVE: ∃d.short'(a,d)
b. EVALUATIVE: ∃d.short'(a,d) ∧ d > s'()*$
However, these non-evaluative readings do not seem to be available. Positive
constructions, as we’ve seen, seem to always be evaluative. Notice though that the
non-evaluative interpretations both assert something very trivial about Amy: that
she has a height (a degree of tallness and shortness, respectively). We can imagine
that such an interpretation is out for pragmatic reasons, making the evaluative
interpretation of the positive construction much more salient.
There are in fact instances of the positive construction being given a nonevaluative interpretation. In ‘exceed’ comparatives, the positive form introduces
the scale on which the two arguments are being compared.5
(29)
Mti hu ni mrefu ku -shinda ule
tree this is big INF -exceed that
‘This tree is taller than that tree.’
Swahili (Stassen 1985: 43)
4
Remember that EVAL occurs with sets of degrees, so each adjective in (26b) introduces a
distinct and co-indexed EVAL (and has a corresponding contextual standard).
5
Thanks to Pam Munro and Russ Schuh for pointing out the significance of this data.
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Jessica Rett
In (29), the positive construction in the first clause (‘This tree is big’) contributes
to the comparative construction by establishing the dimension of measurement on
which the ‘exceed’ relation is calculated. Despite this, (29) can receive a nonevaluative reading, just like English comparatives. It can be used to discuss the
heights of two relatively short trees.
On the other hand, this explanation for the evaluativity of the positive
form predicts that any positive construction can have a non-evaluative
interpretation whenever this reading is not trivial. For instance, it predicts that the
sentence Sue is (once again) heavy/light can be meaningfully uttered to describe
the absence of weightlessness after Sue’s reentrance into the Earth’s atmosphere,
despite Sue being relatively light, or the lightest of the astronauts on the mission.
Although my intuitions waiver, I suspect that this construction cannot be
so used. If that is the case, then it is possible that the restriction against using
positive constructions could be due to a general pragmatic preference against
ambiguity. In the astronaut example, then, the use of Sue is heavy to describe her
absence of weightlessness is blocked by e.g. the less ambiguous Sue (once again)
has a weight, although this is not an entirely satisfactory explanation.
The general conundrum is this: both positive constructions and
constructions with overt degree morphology exhibit evaluativity. The positive
construction seems to do so obligatorily – with a few exceptions, i.e. (29) – and
constructions with overt degree morphology seem to do so optionally. A general
account of evaluativity, then, has to decide which is a primary characteristic of
evaluativity and which is secondary. I am confident given the discussion above
that a successful analysis of evaluativity characterizes it as optional and derives
any obligatoriness secondarily, via pragmatics.
There is one other way in which the manifestation of evaluativity differs in
the positive construction from constructions with overt degree morphology: in the
type of meaning it contributes. For all intents and purposes, evaluativity in the
positive construction is assertive: it can be directly denied (30), and it does not
project out of the antecedent of a counterfactual (31)
(30)
a. Amy is tall.
b. No, she’s not, she’s below the average height for women her age.
(31)
If Amy were tall, she would be a supermodel. # Amy is tall.
This appears to be incompatible with the type of meaning contributed by
constructions with overt degree morphology; for these constructions, evaluativity
seems to be presuppositional.
(32)
(33)
A: Amy is as short as Betty.
B: No, she’s not, she’s taller than Betty.
B':*No, she’s not, she’s actually taller than the average height.
If Amy were as short as Betty, she would not win. " Betty is short.
Antonymy and Evaluativity
This is another instance in which evaluativity behaves differently for the two
different sorts of constructions, and an optimal solution would be able to derive
one behavior from the other. I take evaluativity to be assertive, staying true to its
behavior in the positive construction. As I’ve defined the comparative and the
equative – in terms of relations between sets of degrees – the fact that evaluativity
comes out as a presupposition in these constructions falls out of the semantics of
degree quantifiers and a presupposition that the sets of degrees are non-empty.6
To sum up, evaluativity in the positive construction differs from
evaluativity in constructions with overt degree morphology. These differences can
be reconciled by assuming that the positive construction is [–E], but is almost
always interpreted as evaluative for pragmatic reasons; and that evaluativity is
assertive, but passes presupposition tests in constructions with overt degree
morphology because of the semantics of these quantifiers.
5. Localizing the Competition
The analysis above relies on the notion of semantic competition to determine
which forms can enter a markedness competition. I’ve assumed above that
semantic competition occurs between two mutually entailing expressions. This is
what allows for markedness to effect the evaluativity of polar-variant forms. The
theory as it stands incorrectly predicts that (34a) and (34b) enter into a semantic
competition.
(34)
a. Amy is shorter than Betty.
b. Betty is taller than Amy.
These two forms differ in the polarity of their predicate and the value of their
individual arguments. They are mutually entailing. The fact that (34a) includes the
predicate short means that it is more marked than (34b). The analysis above
predicts, then, that the non-evaluative interpretation of (34b) suffices to block the
non-evaluative interpretation of (34a), which would render (34a) evaluative. This
is the wrong prediction. For some reason, the relationship between (34a) and
(34b) doesn’t result in a semantic competition for the purpose of evaluativity.
It seems reasonable to conclude that this difference (the fact that 34a,b
don’t result in a competition but 22,23 do) is correlated with the fact that (34a,b)
differ from each other additionally in the order of their arguments. The same sort
6
(33) demonstrates that only the evaluativity of the degree clause (Betty’s height) is projected
in an if-clause. Even though the semantics of the equative asserts that Amy and Betty are the same
height, this is an asymmetry. This may be due to the fact that the degree clause itself is
presuppositional, rendering the evaluativity in the degree clause part of a larger presupposition.
Thanks to Roger Schwarzschild for this idea; see von Stechow (1984) for an analysis of the
comparative compatible with this suggestion.
221
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Jessica Rett
of problem can arise with tests for the monotonicity of an argument of an
individual quantifier. To test e.g. the left argument, the quantifier and its right
argument need to be held fixed while the left argument is changed. To vary the
left argument and e.g. the quantifier is to render the test ineffective.
We can imagine that the same sort of test holds for testing the polar(in)variance of a quantifier: a competition that crucially involves the polar(in)variance of a quantifier needs to be constrained in such a way that its
arguments are held constant and only the quantifier is varied. We can do this by
localizing the competition to a subcomponent of the degree construction: one that
minimally involves the quantifier and the predicate.
Assuming a structure in which the quantifier and predicate form a
constituent (Abney 1987, Larson 1988, Corver 1997, Kennedy 1999, Grosu &
Horvath 2006), the compositional semantics are as follows:
{d":+(a,d")} ⊃ {d#:tall'(b,d#)}
(35)
λx[{d":tall'(x,d")} ⊃ {d#:tall'(b,d#)}]
DegP {d":tall'(x,d")} ⊃ {d#:tall'(b,d#)}
NP,
Amy
{d#:tall'(b,d#)}
λx
λD#[{d":tall'(x,d")} ⊃ D#]
Deg'
than Betty is d#-tall
{d":tall'(x,d")}
Deg
!
t,!
AP
-er
tall
This is not an evaluative expression, but if it were, ! marks where EVAL would
be located in the tree.
This configuration gives us a way of isolating the effects of the degree
quantifier and the predicate. We can restrict the semantic competition from
equivalent CPs to equivalent Deg's. Establishing semantic equivalence between
Deg's requires a generalized notion of entailment:
(36)
∀f,g ∈ D!-.$": f ! g iff ∀x ∈ D-, f(x) " g(x)
The two equatives Amy is as short as Betty and Amy is as tall as Betty, for
instance, can enter into a semantic competition in this new sense because their
DegPs are mutually entailing in a generalized sense.
Antonymy and Evaluativity
(37)
a. λD#[{d":short'(x,d")} = D#] "%λD#[{d":tall'(x,d")} = D#]
b. λD#[{d":short'(x,d")} ⊃ D#] "%λD#[{d":tall'(x,d")} ⊃ D#]
Because this theory differentiates between sets of ‘tall’ degrees and sets of
‘short’ degrees, the two Deg's in (37a) aren’t equivalent. If Amy is 5ft tall,
remember, her ‘tall’ degrees are {1ft, 2ft, 3ft, 4ft, 5ft}$%&& and her ‘short’ degrees are
{5ft,6ft,7ft,8ft,…}'()*$. However, the fact that tall and short are polar antonyms
enables us to infer from x’s degrees of tallness to x’s degrees of shortness. In this
sense, then, the set of degrees that are equal to x’s ‘short’ degrees mutually entails
(in a general sense) the set of degrees that are equal to x’s ‘tall’ degrees. Not so for
polar-invariant constructions like the comparative, in (37b): despite any inference
from ‘short’ degrees to ‘tall’ degrees, the two Deg's in (37b) are not mutually
entailing.
Localizing the competition in this way has the added benefit of accounting
for the perhaps surprising evaluativity of modified equatives.7
(38)
a. Amy is at least as short as Betty.
b. Amy is almost as short as Betty.
The sentences in (38) are evaluative, presumably because they involve the
quantifier as. However, the fact that they are modified e.g. by at least means that,
semantically, they are more like the comparative (the proposition Amy is at least
as short as Betty, even under the ‘exactly’ semantics of the equative, does not
mutually entail Amy is at least as tall as Betty). The current account captures the
intuition that all equatives are evaluative, regardless of how they are modified, by
restricting the competition to the Deg'.8
To summarize: the previous section described the distribution of
evaluativity in terms of a competition, which dealt with entailment at the
propositional level. The pair in (34), along with the evaluativity of modified
equatives like Amy is at least as tall as Betty, demonstrate that the competition
needs to be localized. Given that the two factors that determine the distribution of
evaluativity are the polarity of the predicate and the polar-(in)variance of the
quantifier, I've reasoned that the area of localization is the Deg' in which the
predicate and quantifier form a constituent. Adapting the notion of generalized
7
Thanks to Hans Kamp (p.c.) for bringing this problem to my attention.
Daniel Büring (p.c.) has pointed out that factor modifiers differ from e.g. at least and almost
in that they don't preserve the ealuativity of [+E] constructions.
8
(i) Amy is twice as short as Betty, but neither woman is short.
This seems to be evidence that factor modifiers are base-generated in Deg' and, unlike at least and
almost, can effect the semantics of the construction for the competition. I do not currently know
enough about the syntax and semantics of factor modifiers to be able to explain this very
interesting difference.
223
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Jessica Rett
entailment between objects of type !!d,t",t" and drawing on the important relation
between polar antonyms is sufficient to preserve the results that made the
proposition-level account successful.
6. A Typology of Gradable Adjectives
Until now, the main focus of this paper has been the distribution of evaluativity
among degree constructions with the antonyms tall and short. With these
antonyms, degree constructions display the evaluativity pattern shown in (8);
however, the presence of different types of antonyms effects the pattern of
evaluativity across degree constructions.
(39)
(40)
(41)
a.
b.
a.
b.
a.
b.
Amy is taller than Betty. # Amy is tall.
Amy is shorter than Betty.%# Amy is short.
This glass is cleaner than that glass. # This glass is clean.
This glass is dirtier than that glass. " This glass is dirty.
This glass is more opaque than that glass. " This glass is opaque.
This glass is more transparent than that glass. " This glass is transparent.
Looking at just the comparative construction for simplicity’s sake, we get
three different patterns: 1) antonyms like tall and short whose comparative forms
are never evaluative; 2) antonyms like clean and dirty whose positive comparative
form is not evaluative, but whose negative comparative form is; and 3) antonyms
like opaque and transparent, whose comparative forms are both evaluative.
Rotstein & Winter (2004) and Kennedy & McNally (2005) observe that
scales associated with different gradable adjectives differ in scale structure: they
can have only a lower bound, only an upper bound, be completely open or
completely closed.
(42)
(43)
(44)
Open scales
a. ??perfectly/??slightly tall
Lower/upper closed scales
a. ??perfectly/slightly dirty
Closed scales
a. perfectly/slightly opaque
b. ??perfectly/??slightly short
b.
perfectly/??slightly clean
b. perfectly/slightly transparent
In relation to these scale structures, Kennedy (2007) postulates an
economy principle: “Maximize the contribution of the conventional meanings of
the elements of a sentence to the computation of its truth conditions.” The
assumption of this economy principle explains the connection between these
predicates’ scale structures and evaluativity patterns: because the scales associated
Antonymy and Evaluativity
225
with e.g. tall and short lack bounds, their standards must be contextually
determined. Adjectives associated with bounded scales have natural standards in
their endpoints, and these become the value of the standard.
s
s
tall/short
dirty
s
clean
s
opaque/transparent
Figure 2: Scale structures and standard placement
If we assume that EVAL has the same optional distribution, the
evaluativity patterns demonstrated in (42) through (44) fall out of the different
structures of the scales associated with the predicates. Constructions with closedscale adjectives (44) and lower-bound adjectives (43a) are always evaluative
because their standard always corresponds to their lower bound: to be on the scale
is to be above the standard on the scale, with or without EVAL. Constructions
with upper-bound adjectives (43b) are never evaluative because their standards
are set at their upper bound. To be on the scale is to be below the standard on the
scale, with or without EVAL. This demonstrates that a degree-modifier analysis of
evaluativity can account for the distribution of evaluativity across all gradable
predicates: the distribution of EVAL is held constant, but its effects differ based
on the structure of the scale invoked by the construction.9
7. Conclusion
I have shown that the distribution of evaluativity is too wide to be accounted for
with a morpheme that is in complementary distribution with overt degree
morphology (e.g. POS). However, the distribution of evaluativity is too narrow to
be accounted for with a degree modifier like EVAL, unless we make additional
assumptions about polarity and polar-invariance. The polar-(in)variance of a
quantifier determines whether or not the polarity of the predicate will affect a
construction’s non-evaluative interpretations.
9
‘Extreme adjectives’ (Paradis 2001) are those like gorgeous and brilliant which behave like
closed-scale and lower-bound adjectives in being evaluative even in comparative constructions. I
assume that this is because they are associated with subscales of those scales like ‘pretty’ and
‘smart,’ which gives them a natural lower bound like these other predicates.
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Jessica Rett
There is a debate about whether the equative has an ‘at least’ reading (a
weak reading) or an ‘exactly’ reading (a strong reading). From Horn (1972):
(45)
Amy is as tall as Betty.
a. No, she’s not, she’s taller.
b. Yes, in fact, she’s taller.
The traditional way to derive a weak/strong ambiguity is to assign the form the
weak reading and to derive the strong reading pragmatically, via scalar
implicature (however, see Fox 2006).
Where evaluativity is concerned, the issue is simple: equatives and
comparatives simply behave differently with respect to evaluativity, and we can
give a good account of why equatives pattern with questions rather than with the
comparative if we assume it has an ‘exactly’ meaning (or a still weaker meaning
which can become either ‘exactly’ or ‘at least’ with the presence of a modifier, as
in Schwarzschild & Wilkinson 2002 and Bhatt & Pancheva 2007). Whatever the
solution is, I believe that the distribution of evaluativity and the encouraging
success of this analysis suggests that we have an empirical reason to distance the
equative from its ‘at least’ interpretation.
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